The value of (e^(-π/4) + ∫₀^(π/4) e^(-x)tan⁵⁰x dx)/(∫₀^(π/4) e^(-… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 13 April, Shift 2Definite Integrals

The value of $\dfrac{e^{-\frac{\pi}{4}} + \displaystyle\int_{0}^{\frac{\pi}{4}} e^{-x}\tan^{50}x \, dx}{\displaystyle\int_{0}^{\frac{\pi}{4}} e^{-x}\left(\tan^{49}x + \tan^{51}x\right) dx}$ is:

A
$25$
B
$51$
C
$50$
D
$49$

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